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Abstract
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Knutson, Tao, and Woodward (2004) formulated a Littlewood–Richardson
rule for the cohomology ring of Grassmannians in terms of puzzles.
Vakil (2006) and Wheeler and Zinn-Justin (2017) have found additional
triangular puzzle pieces that allow one to express structure constants for
-theory
of Grassmannians. Here we introduce two other puzzle pieces of
hexagonal shape, each of which gives a Littlewood–Richardson rule for
-homology
of Grassmannians. We also explore the corresponding eight versions of
-theoretic
Littlewood–Richardson tableaux.
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Keywords
puzzles, hexagon, tiling, K-theory, Grassmannian,
Littlewood–Richardson coefficient
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Mathematical Subject Classification 2010
Primary: 05E15
Secondary: 14M15, 52C20
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Milestones
Received: 3 April 2018
Revised: 3 March 2019
Accepted: 1 May 2019
Published: 4 January 2020
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